A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

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How did Einstein arrive at the right hand side of his general relativity tensor equation?

It seems Einstein postulated the right hand side of his field equations… I see in books that tell the story of how he arrived at what to put on the right hand side of his tensor equations, the physics ...
2
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2answers
911 views

Curvature of spacetime as a real thing?

I get the curvature tensor in General Relativity, it is “just” math. Does space-time REALLY curves as a tangible thing, or is Einstein proposing a mathematical abstraction? More naively, please allow,...
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3answers
197 views

What is the evidence of interpreting $g_{\mu\nu}$ as the metric of space-time?

I think if we don't mention the meaning of $g_{\mu\nu}$ as the metric of space-time, we can still construct the equation of motion and Einstein field equation in a way such that $g_{\mu\nu}$ is just a ...
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1answer
76 views

Flatness and Kinetic Energy

Why the curvature parameter can be interpreted as the difference between the average potential energy and the average kinetic energy of a region of space? Curvature parameter:$$\Omega_{k}\equiv\Omega-...
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168 views

Does gravitational time dilation affect apparent mass?

Suppose I'm on a highly elliptical orbit around some massive body. As I get closer, I start to experience time dilation due to the object's gravitational field - time starts passing slower for me than ...
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2answers
123 views

Time Dilation Properties

I've read up on time dilation and how gravitational/kinematic time dilation work but I have not received a clear answer on how the two work together. If you are observing something traveling at a ...
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2answers
1k views

Spacetime geometry around two black holes

For space-time geometry we all know images like he one below. But if I were to take a neutron star and put it right next to but not touching a black hole what effect would that have on the geometry of ...
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2answers
717 views

Feynman's statement of the Einstein Field Equations

In Feynman's Lectures on Physics (Volume 2, chapter 42) he states that Einstein's field equation is equivalent to the statement that in any local inertial coordinate system the scalar curvature of ...
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1answer
104 views

Post-Newtonian acceleration formula

First of all, I have to say that I know very little about tensors and partial differential equations, as I've never done them at school. I'm developing an application which simulates the motion of ...
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4answers
100 views

Effect of expansion on time?

We know that for moving body times moves at a slower rate, but can this happen for Universe itself whose rate of expansion is accelerating?
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37 views

Where does the dark energy of space expansion come from? [duplicate]

Space has a constant density of dark energy, that means dark energy does not dilute with space expansion. By consequence, any space generated by space expansion does generate new dark energy. ...
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3answers
332 views

why do x Schwarzschild radii equal time dilation effects of speed of light going y times faster than an object^2?

let me walk you through the math. First you start with the gravitational time dilation formula where: $$ T_1=T\sqrt{1-\frac{2GM}{rc^2}} $$ and rather than entering $r$ for the radius we replace $r$ ...
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2answers
453 views

Is space stretched with no limits by a black hole?

Some depictions of black holes show space being warped into a singularity, with no end, e.g. as pictured below. Moreover, in Cosmos, Neil Tyson speculates with the possibility that Black Holes contain ...
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2answers
140 views

Is the surface of a heavy sphere bigger than $4 \pi r^2$ due to general relativity?

I am unfortunately not familiar with the mathematics behind general relativity. However, on a heavy planet (say a sphere) gravity will bend space-time in a way that an object initially in rest, will ...
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3answers
2k views

Event Horizon of Supermassive Black Holes

I'm going to ask/explain this as best I can; I'm sure I have some fundamentals wrong here. Spaghettification is a phenomenon which occurs only in stellar-mass black holes owing to the immense gravity ...
4
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2answers
240 views

Is gravity a force? [duplicate]

If gravity just emerges from the curvature of spacetime, is it actually a force? Why is it one of the 4 fundamental forces of nature?
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1answer
405 views

Time coordinate inside black hole horizon [duplicate]

I am new to physics and was trying to learn more especially about general relativity. The Schwarzschild metric, changes the sign of the time and radial parts of the metric once we cross the event ...
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5answers
896 views

Does coordinate time have physical meaning?

I have always been a little confused by the meaning of the "$t$" which appears in spacetime intervals or metrics in general relativity. I concluded that $t$ was just a mathematical thing which allow ...
6
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1answer
249 views

Null Coordinates

I have a very basic question: what are the advantages of writing a metric in the null coordinates? Which extra insight do they provide? I've looked in Caroll's "Spacetime and Geometry" and Wald's "...
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0answers
148 views

Energy-momentum tensor

I need to show that: \begin{align} \mathcal h_i^a \, T_{ab} \, h_i^b=(\nabla_i \phi)^2-\frac{h_{ii}}{2}[\dot{\phi}^2-(\nabla \phi)^2-m^2 \phi^2] \end{align} where i) $T_{ab}=\nabla_a \phi \...
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1answer
199 views

Are a black hole really connecting 2 parallel universe?

What is beyond the point of singularity in a black hole and universe expands in all the 3 $x$, $y$ and $z$ axis? So how can one thing be on top of another when we don't know where the end point of ...
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1answer
118 views

How is $\Omega_0 = 1$ when the characteristic “teardrop” past light cone seems to admit curvature?

Introduction: The top graphic is just one I pulled from a page describing the process of detecting cosmic curvature. The second graphic is one I drew up to illustrate my misunderstanding. My ...
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2answers
323 views

Curved space-time VS change of coordinates in Minkowski space

I'm looking for a rather intuitive explanation (or some references) of the difference between the metric of a curved space-time and the metric of non-inertial frames. Consider an inertial reference ...
5
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2answers
240 views

Can we test QFT on a curved spacetime?

It is possible to extend a quantum field theory to a curved spacetime. But does this lead to predictions that can be tested and measured? Had it been confirmed? The underlying reason I am asking this ...
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2answers
305 views

Particles inside black hole does not hit singularity

We say that if any particles from outside fall into the black hole, they eventually hit singularity. Then why not particles already inside the black hole are at singularity? Or are they? If yes, then ...
5
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2answers
158 views

How to prove explicitly that by including Dirac fermions into the Einstein-Hilbert action we make torsion to be non-zero?

Recently I've heard the statement that by including Dirac fermions into the Einstein-Hilbert action we make torsion be non-zero, so that is one of problem of quantum gravity. How to prove that ...
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1answer
327 views

Relationship between mass and the radius of curvature of space and time

What is the relationship between mass and the radius of curvature of space and time created due to the presence of the mass? please give the mathematical relation if there is any?
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1answer
149 views

Why gamma-matrices are associated with tetrads Lorentz rotation?

In Zee's "QFT in nutshell" in a paragraph "Differential geometry of Riemann manifold" he states that Dirac gamma-matrices are associated with tetrads Lorentz rotation, so Dirac lagrangian in curved ...
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2answers
258 views

Raising and Lowering indices of tensor

Why we use metric tensors $g$ to raise or lower indices of tensors, why not using other (invertible) order-2 tensors to do the job?
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1answer
112 views

Proof of expression to combine different redshifts

I am trying to arrive to the following expression: $1+z = (1+z_C)(1+z_G)(1+z_D)$ so the total redshift is the product of the cosmological redshift, the gravitational redshift and the Doppler ...
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3answers
839 views

How does a rotating object cause frame dragging?

Frame dragging is a consequence of general relativity. But I don't really understand it. Of course I can find metaphors like the "honey metaphor" where stirring a honey can move the specks even if ...
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2answers
237 views

Can we add two singularities and make a single singularity? [duplicate]

My question is if we have two black hole and they will merge into each other, then where will be the singularity?
2
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1answer
591 views

If space warps distort moving objects' trajectories, does it mean that static objects are immune to gravity? [closed]

If gravity is just space distortion, which affects trajectories of moving objects, then a static object (not moving, thus no trajectory) will not suffer any type of accelerating force from gravity? ...
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1answer
179 views

Can the Alcubierre Drive be explained by Gravitoelectromagnetism? [closed]

Even though there is no experimental evidence, that the Alcubierre drive works. The Einstein field equations permit this solution. For Gravitoelectromagnetism there are hints and ongoing efforts to ...
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2answers
88 views

The abstract space of metrics in GR

I know this is a general (har har) question, but has any work been done understanding the mathematical space the allowed metrics in GR form? (I guess it'd be called a tensor space???)
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0answers
91 views

What is the relationship between the formal definition of a tensor and the frequently discussed notion of a “higher order matrix”?

I've been doing some self study on the principles of tensors & manifolds in preparation for a first course in general relativity. I tend to learn better when presented with the full mathematical ...
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1answer
149 views

Physical visualisation of curvature

I was wondering-how do you visualise curvature in the context of general relativity. The gravity well and trampoline analogies are quite wrong, so I want a more realistic approach to it (say, the way ...
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0answers
95 views

Will relativistic glider cause lower gravitational force in Newtonian gravitation?

In the articles The relativistic glider and The relativistic glider revisited, the relativistic glider is proposed where a quasi-rigid body can slow down its fall under gravity without any reaction ...
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148 views

What is the action for a photon? [duplicate]

If I understand correctly, the action for a massive free particle is: $$ S = -mc^2 \int \mathrm{d}\tau = -mc \int \sqrt{g_{\mu\nu} \frac{\mathrm{d}x^\mu}{\mathrm{d}\lambda} \frac{\mathrm{d}x^\nu}{\...
6
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1answer
442 views

Can gravitational waves orbit each other to form a standing wave?

Since gravitational waves are a type of propagation of energy of some sort, they ought to induce their own gravitational field. I'm assuming this extra gravitational force / curvature is independent ...
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1answer
127 views

Spacetime Metrics and Quantifying Length of a Spacetime Curve

On page 247 in Gravitation by Misner, Thorne, and Wheeler, they state: "No metric means no way to quantify length; nevertheless, parallel transport gives a way to compare length!" Three questions: ...
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3answers
683 views

Visualizing GR spacetime distortion in 1+1D spacetime instead of 2D space

Usually spacetime distortion due to mass in GR is visualized as a rubber sheet distorted under some massive object, like this: source or as shown in this link. But what has always bothered me is ...
2
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1answer
69 views

Is there any difference in radiation pressure for two observers in different gravitational potential?

Suppose that a light beam is shone upwards from surface of a planet. So, due to gravitational redshift, the frequency of the light perceived by observer far from the surface will be lower than that ...
6
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2answers
320 views

Is a local Lorentz frame a coordinate chart on a spacetime manifold?

I am just starting to learn GR. I'm alternating between studying physics books and studying math books. I keep seeing the term Lorentz frame and I'm not sure what it means mathematically. Is a ...
2
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0answers
108 views

What's the physical or mathematical meaning of considering non-minimal coupling?

Why we still consider the case of non-minimal coupling? And I don't really understand the motivation of coupling. In general relativity, the non-minimal coupling violates the principle of equivalence....
2
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1answer
152 views

Can two distinct events occur at precisely the same moment in time?

I am writing a simulation and am having difficulty resolving the order in which two distinct forces occur. The simulation will give different results if the forces are applied to the state in ...
3
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1answer
207 views

Gravitational coupling of tachyons

Can General Relativity stress-energy tensor be extended to include contributions from imaginary mass tachyons? what would be the expected gravitational coupling between tachyons and tardions?
0
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1answer
123 views

A Theory of Almost Everything? [closed]

Before I present this theory, I ask that you take the time to read this disclaimer. I do not claim to have an excellent knowledge of physics, it is actually rather limited. Therefore, I am not ...
4
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1answer
284 views

The arrow of time and the cosmology of a black hole interior

When solving the Einstein field equations in Schwarzschild metric for an observer falling into a black hole the radial coordinate r of the black hole and time t switch roles in the equations when r<...
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0answers
104 views

Is time depending on the observer in string theory?

I heard that in the theory of relativity the time of an action is depending on the observer. But in string theory, is the time also depending on the observer? Are strings acting according to the ...